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fsc-part1-ptb:important-questions:ch07-permutation-combination-and-probablity [2021/02/07 16:47] (current) – created - external edit 127.0.0.1
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 +====== Ch 07: Permutation, Combination and Probability ======
 +<list-group>
 +  * Find $n$ when ${^nC_{12}}={^nC_6}$ ---// BISE Gujranwala(2015)//
 +  * Evaluate  ${^{20}C_{17}}$ without calculator ---// BISE Gujranwala(2015)//
 +  * How many $6-digit$ numbers can be formed from the digits $2,2,3,3,4,4$? How many of them with lie between $400,000$ and $430,000$?  ---// BISE Gujrawala(2015)//
 +  * How many words can be formed from the letter $``PLANE"$ using all letters (no letter is repeated)  ---// BISE Gujrawala(2017)//
 +  * Prove that $^nC_4=^nC_{n-r}$ ---// BISE Gujrawala(2017)//
 +  * Find the numbers of diagonals of a $6-digits$ figures  ---// BISE Gujrawala(2017)//
 +  * A coin is tossed four times, find the probability that top shows all heads. ---// BISE Gujranwala(2017)//
 +  * Show that $n^3-n$ is divisible by $6$ for $n=2,3$ ---// BISE Gujrawala(2017)//
 +  * Find the value of $n$ when $^nP_2=30$ ---// BISE Sargodha(2015)//
 +  * Find numbers of diagonals of $6-dided$ figure. ---// BISE Sargodha(2015)//
 +  * Find the value of $n$. $^nC_{12}=^nC_6$ ---// BISE Sargodha(2015)//
 +  * Determine the probability of getting two heads in two successive tosses of a coin? ---// BISE Sargodha(2015)//
 +  * Prove that $^{n-1}C_r+^{n-1}C_{r-1}=^nC_r$ ---// BISE Sargodha(2015)//
 +  * If $\frac{a_5}{a_3}=\frac{4}{9}$, $a_2=\frac{4}{9}$ in $G.P$. Find $a_n$ ---// BISE Sargodha(2015)//
 +  * Find $n$, when $^{11}P_n=11.10.9$---// BISE Sargodha(2015), BISE Sargodha(2016) //
 +  * In how many way can a hockey team of $11$ be selected out of $15$ players. ---// BISE Sargodha(2015)//
 +  * A die is thrown. Find the probability that the dots on the top are prime number or odd number. ---// BISE Sargodha(2015)//
 +  * The sum of $9$ teams of an $A.P.$ is $171$ and its eighth team is $31$. Find the series. ---// BISE Sargodha(2015)//
 +  * Prove that $^nC_r+^nC_{r-1}=^{n+1}C_r$  ---// BISE Sargodha(2015)//
 +  * Find the sum of $\frac{9}{4}+\frac{3}{2}+1+\frac{2}{3}+...\infty$ ---// BISE Sargodha(2016)//
 +  * Evaluate $^{20}C_{17}$ ---// BISE Sargodha(2016)//
 +  * Prove that $^{n-1}C_r+^{n-1}C_{r-1}=^n C_r$  ---// BISE Sargodha(2016)//
 +  * Prove that $^nC_r=^nC_{n-r}$  ---// BISE Sargodha(2017)//
 +  * In how many ways can $4$ keys be arranged on a circular key ring?  ---// BISE Sargodha(2017)//
 +  * How many words can be formed from the letters of the word $``objective"$ using all letters without repeating anyone?  ---// BISE Lahore(2017)//
 +  * Find the values of $n$ and $r$ when $^nC_r=35$ and $^nP_r=210$  ---// FBISE(2016), BISE Lahore(2017)//
 +  * If $S=\{1,2,3,...9\}$, Even $A=\{2,4,6,8\}$, $B=\{1,3,5\}$. Find $P(A \cup B)$ ---// BISE Lahore(2017)//
 +  * A die is thrown. Find probability that the dots on the top are prime numbers or odd numbers. ---// BISE Lahore(2017)// 
 +  *  Find the values of $n$ and $r$ when $^{n-1}C_{r-1}:^nC_r:^{n+1}C_{r+1}=3:6:10$  ---// FBISE(2017)//
 +  * Show that sum of $n$ $AM's$ between $a$ and $b$ is equal to $n$ times their $AM's$ ---// FBISE(2017)//
  
 +</list-group>
 +{{tag>FSc FSc_Part1 Important_Questions_FSc_1}}